Efficient linearized local energy-preserving method for the Kadomtsev-Petviashvili equation | Zendy

Jiaxiang Cai | Zendy; Juan Chen | Zendy; Min Chen | Zendy

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Efficient linearized local energy-preserving method for the Kadomtsev-Petviashvili equation

Author(s) -

Jiaxiang Cai,

Juan Chen,

Min Chen

Publication year - 2021

Publication title -

discrete and continuous dynamical systems - b

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.864

H-Index - 53

eISSN - 1553-524X

pISSN - 1531-3492

DOI - 10.3934/dcdsb.2021139

Subject(s) - symplectic geometry , discretization , mathematics , scheme (mathematics) , backward euler method , hamiltonian (control theory) , euler's formula , soliton , mathematical analysis , nonlinear system , mathematical optimization , physics , quantum mechanics

A linearized implicit local energy-preserving (LEP) scheme is proposed for the KPI equation by discretizing its multi-symplectic Hamiltonian form with the Kahan's method in time and symplectic Euler-box rule in space. It can be implemented easily, and also it is less storage-consuming and more efficient than the fully implicit methods. Several numerical experiments, including simulations of evolution of the line-soliton and lump-type soliton and interaction of the two lumps, are carried out to show the good performance of the scheme.

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